> I think what we're forgetting is that practice only engages the >student on a "lower-level" thinking platform. Unless we include opportunities for students to stretch their thinking >though tasks like the "24 game", then students will never move >beyond rote memory and practice. To define more challenging >mathematics tasks as the role of supplementary material or activities scares me. >Why? Because, many will say they don't have time for the supplemental materials. Their students will be relegated to >the math that machines can do all their life.
Please don't let me "scare" you. And I hate to think I'm "relegating" my students to a lifetime of anything. The problem is how do you get kids to be able to solve the mathematical problems they will face for their lifetime. After only ten years of teaching, I've come to the conclusion that students will best be prepared for a lifetime of math if they learn in a well structured curriculum accumulating a reservior of concepts and algorithms they can bring to bear on problems. And as a part of that curriculum, we should practice exactly that on problems sometimes provided by materials representing the strands of the Calif. framework and the NCTM standards. Only problem I have is that I don't think working from the specific problem to the general skill works as well.
> I think Battleship is an excellent way to introduce the >coordinate system. It's highly motivating and meaningful. We >are graphing for a purpose. Most American kids do remember >what they do from day-to-day if it is interesting. Having been >a middle school mathematics teacher for 33 years, I can assure >you that the more activities in mathematics that I can associate with a game, the more the skills stay and are remembered.
Did I say "Battleship" was a bad thing? (Although, I don't think we should burden our children with the militarism of our past. How about we call it "Conservative Republicans". Something really worth torpedoing!! :) And, no, I don't think engaging in something interesting is a total remedy for kids who have trouble remembering. The principle is important, but not something on which to base an entire curricula. I know it goes against the overriding American need to be entertained, but most learning is based on old fashioned hard work and study. > > > > So please. I do know how the standards incorporates practice, most often to > > solve irresistibly interesting problems and I simply don't think it works > > very well. High schools in LA which are thought to have the most > > "progressive" math departments also seem to have some pretty abysmal scores > > on the CLAS test, a test written by and for the reformers. > > Until the curriculum and pedagogy change so that the CLAS test >measures what is being presented in the classroom, the test >will have "pretty abysmal scores." No one believes that kids >in high school at the moment reflect any of the Standards >education. They are too old. Most school systems are barely >implementing the Standards right now. We are also just >learning now how to serve the needs of a diverse population >which is reflected in our cities. I suggest we look at the >next six years and see.
My point wasn't that their radical reforming isn't showing. In fact, their students appear to be doing more poorly than schools continuing with the traditional curricula. And this is on the CLAS test which was designed and implemented by the reformers. > > And as far as research is concerned, I don't have much faith in it, given the > > nature of our universities (particularly education departments) and the fact > > good teachers can make most any curriculum sing. > >
>And every good teacher I know does not stay with one >curriculum. She is eclectic and picks what is known to work. >I believe this is what the Standards suggest.
Then I guess the NCTM doesn't have a problem with the Saxon books. Glad to hear it.
> > Give me field testing of different schools and mediocre teachers like most of > > us with classes of forty kids on standardized tests that can be studied for. > > (Sorry for ending my sentence with a preposition. I am a math teacher) Then > > we'll see what's working and what isn't. > > > >In my 33 years of teaching I have not met "mediocre" teachers. >Our mathematics educators are dedicated and anxious to help >their students. It is self-defeating to look at ones self as >mediocre. And, I teach mathematics and don't use it as an >excuse for poor grammar. You can't. Students must see the >math teacher as competent in all areas. In fact, students must >see that writing is important to mathematics, whether it may be >technical writing or expository writing.
You've never seen a "mediocre" math teacher ? I wonder what that does to the average? As Ted Kennedy once said "I want to live in an America where all the people earn more than the average". P.S. I was kidding about writing.
> > It seems to me the standards folks would be thrilled to finally demonstrate > > the efficacy of their curricula. Again, I'd recommend you read "Class > > Action", a new book on what I'm discussing. > > > >The Standards do not proscribe curricula. They "guide" >educators to what is felt to be the appropriate emphasis on >content; and, they suggest pedagogy.
Would you agree there are curricula which are more in line with the standards? And wouldn't you like to see them compared against objective criteria, because unless you know something I don't, I haven't seen a scintilla of evidence that the more radical stuff has had any success.